Using a nonlinear mixed logit model, this study investigates commuter choice behaviour in the presence of uncertain travel time. Within the proposed source-dependent extended expected utility framework, the uncertainty-risk gap is captured in the source function and the attitude towards ambiguity is measured over the full subjective probability distribution. Based on one revealed preference dataset, we structurally estimated observed heterogeneity in ambiguity attitudes in terms of socioeconomic covariates and unobserved between-subject heterogeneity in taste preferences, while controlling for risk attitude and allowing for the trade-off between attributes. In addition to revealed age and gender differences in ambiguity preferences, other important findings include partial ambiguity seeking in this type of loss domain and the existence of likelihood insensitivity under uncertainty (i.e., a-insensitivity). This systematic investigation of decision making under uncertainty in real-market settings would offer behaviourally realistic inputs into the evaluation of social effects and design of effective policies.